Assign action to multiple objects
There are still possible solutions by using some node-based animation addons like Animation nodes and MotionTool. It is hard to cover enough information here on how to use them, but you can learn them from many places, and they are not so hard to learn at all (I'll try cover the basic usage if really requested).

Now let's take a simple case. Assuming you want to render the object(s) during frame 1 to 10, not render during frame 11 to 15, then render again from frame 16, we can use them to do so:

Setup for Animation Nodes:



Setup for MotionTool:





P.S.: You can still insert keyframes for buttons and values on those nodes, which may further simplify the setups, but the animation data haven't been exposed to any editors, which makes it less convenient to control, and not currently recommended.